Cosmic dawn (CD) and the epoch of reionization (EoR) are the most important parts of cosmic history during which the first luminous structures emerged. These first objects heated and ionized the neutral atomic hydrogen in the intergalactic medium. The redshifted 21-cm radiation from the atomic hydrogen providesan excellent direct probe to study the evolution of neutral hydrogen (Hi) and thus reveal nature of the first luminous objects, their evolution and role in this last phase transition of the Universe and formation and evolution of the structures thereafter. Direct mapping of the Hi density during the CD–EoR is rather difficult with thecurrent and forthcoming instruments due to stronger foreground and other observational contamination. The first detection of this redshifted Hi signal is expected to be done through statistical estimators. Given the upmost importance of the detection and analysis of the redshifted 21-cm signal, physics of CD–EoR is considered asone of the objective of the upcoming SKA-low telescope. This paper summarizes the collective effort of Indianastronomers to understand the origin of the redshifted 21-cm signal, sources of first ionizing photons, their propagation through the IGM, various cosmological effects on the expected 21-cm signal, various statistical measures of the signal like power spectrum, bispectrum, etc. A collective effort on detection of such signalby developing e stimators of the statistical measures with rigorous assessment of their expected uncertainties, various challenges like that of the large foreground emission and calibration issues are also discussed. Various versions of the detection methods discussed here have also been used in practice with the Giant MeterwaveRadio Telescope with successful assessment of the foreground contamination and upper limits on the matter density in reionization and post-reionization era. The collective efforts compiled here has been a large part of the global effort to prepare proper observational technique, analysis procedure for the first light of the CD–EoR through the SKA-low.

We propose the intensity mapping of the redshifted Hi 21-cm signal from the post-reionization epoch as a cosmological probe of $f(R)$ gravity. We consider the Hu–Sawicki family of $f(R)$ gravity models characterized by a single parameter $f_{,R0}$. The $f(R)$ modification to gravity affects the post-reionization 21-cm power spectrum through the change in the growth rate of density fluctuations. We find that a radio interferometric observation with a SKA1-mid-like radio telescope in both auto-correlation and cross-correlation with galaxy weak-lensing and Lyman-$\alpha$ forest may distinguish $f(R)$ models from $\Lambda$CDM cosmology at a precision, whichis competitive with other probes of $f(R)$ gravity.